To calculate: To simplify the expression −8x33.

Calculation:
According to quotient property of square root ${\displaystyle \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}}$.
And the product property of square root states ${\displaystyle \sqrt{ab}=\sqrt{a}\cdot \sqrt{b}}$
This can be written as $\sqrt[3]{-8x^3}=\sqrt[3]{(-2)\times (-2)\times (-2)\times x\times x\times x}$
$\sqrt[3]{-8x^3}=\sqrt[3]{(-2{)}^3\times x^3}$
Applying the product rule,
$\sqrt[3]{-8x^3}=\sqrt[3]{(-2{)}^3}\times \sqrt[3]{x^3}$
$\sqrt[3]{-8x^3}=(-2)\times x$
$\sqrt[3]{-8x^3}=-2x$